The last question for this problem is throwing me off. Am I looking at the initial state first then look at the transition state, so is it alpha*P^3?

4. The Smiths receive the paper every morning and place it on a pile after reading it. Each afternoon, with probability 1/3, someone takes all the papers in the pile and puts them in the recycling bin. Also, if ever there are at least five papers in the pile, Mr. Smith (with probability 1) takes the papers to the bin. Consider the number of papers in the pile in the evening. Is it reasonable to model this by a Markov chain? If so, what are the state space and transition matrix? What is the probability that there is 1 paper in the pile in the third evening given initially there is no paper in the pile. ~